Qx was more interested than I but we both were puzzled by some claims some folks have made over the years about the Ashkenazic history. It has clarified a lot of facts for both of us.
We now understand--checking with you here--that the Askhenazic Jews are CERTAINLY as much Jews by ancestry and their ancestry's links to the Levant/Israeli homeland as any other kind of Jew. DNA studies are emphatically conclusive on this score.
Any blather about the Ashkenazi's being converts from an Eastern European non-Jewish ancestry is--essentially--nonsense.
Do we have it right?